I too would like to know if this is possible. It seems that someone posted it as an Idea: https://c.na9.visual.force.com/apex/ideaView?id=087E00000004pEhIAI but that's been merged into a larger issue. Requiring a change of ownership in order to edit a webmap is clumsy, and it doesn't seem that anything has improved in the year since you first posted this question. That's too bad. I'd love to know when/if this feature is implemented.
Hi David,
You can accomplish this by creating a custom role. You can apply 'Update' for Content under Administrative Privileges.